Somatodendritic Currents and
Spike Direction
Channel description
a. Soma and dendrite channels:
We used seven types of ionic channels to simulate the active properties of the somatodendritic membrane: fast sodium (Na+), calcium (Ca++), and five potassium currents: delayed rectifier (DR), small persistent muscarinic (M), A-type transient (A), short-duration [Ca]- and voltage-dependent (C) and long duration [Ca]-dependent (AHP). Conductance variables were described with Hodgkin-Huxley type formalism. The kinetics of all these channels has been obtained from Warman et al. (1994) with the following modifications: Here we reproduce the description of all channels in the standard Hodgkin-Huxley notation:Equilibrium potentials were +45 and -85 mV for Na+ and K+, respectively. The activation time constant for the Na+ channel was still halved due to the faster rising slope of in vivo APs. For the Ca++ channel a 35ºC was used in the Nernst equation, ECa = -13.275Ln([Ca,1]in/[Ca]o), where [Ca]o is 1.2 mM and [Ca,1]in refers to pool number 1 (see the description for the calcium dynamics). For the C-type K+ channel, alphac = -0.0077(Vm+Vshift+103)/{exp[(Vm+Vshift+103)/-12]-1}.
Na channel (Na_Wr):INa = gNam3h(Vm-ENa)
ENa = 45 mV
alpham = -3.48(Vm-11.0)/{exp[(Vm-11.0)/-12.94]-1}b. Axon channels:betam = 0.12(Vm-5.9)/exp[(Vm-5.9)/4.47]-1}
alphah = 3/exp[(Vm+80)/10]
betah = 12/{exp[(Vm-77)/-27]+1}
Ca channel (Ca_W):
ICa = gCas2r(Vm-ECa)
ECa = -13.3Ln([Ca,1]in/1200)
alphas = -0.16(Vm+26.0)/{exp[(Vm+26)/-4.5]-1}
betas = 0.04(Vm+12)/exp[(Vm+12)/10]-1}
alphar = 2/exp[(Vm+94)/10]
betar = 8/{exp[(Vm-68)/-27]+1}
K_C channel (K_C_Wtn):
IC = gCc2d(Vm-EK)
EK = -85 mV
alphac = -0.0077(Vm+Vshift+103)/{exp[(Vm+ Vshift +103)/-12]-1}
betac = 1.7/exp[(Vm+Vshift+237)/30]
Vshift = 40Log([Ca,1]in)-105
tauc = 1.1 ms
alphad = 1/exp[(Vm+79)/10]
betad = 4/{exp[(Vm-82)/-27]+1}
K_AHP channel (K_AHP_Wtn):
IAHP = gAHPq(Vm-EK)
EK = -85 mV
alphaq = 0.0048/exp[(10Log([Ca,2]in-35)/-2]
betaq = 0.012/exp[(10Log([Ca,2]in+100)/5]
tauq = 48 ms
K_M channel (K_K_W):
IM =gMu2(Vm-EK)
EK = -85 mV
alphau = 0.016/exp[(Vm+52.7)/-23]
betau = 0.016/exp[(Vm+52.7)/18.8]
K_Ap channel, proximal K_A type channel (K_A_3):
IAp =gApa4b(Vm-EK)
EK = -85 mV
ainf = 1/{exp[(-Vm-5)/10]+1}
taua = 0.15ms
binf = 1/{exp[(Vm+56)/8]+1}
taub = 5ms if Vm<-30 mV and 5+0.26(Vm+30) if Vm>30 mV
K_Ad channel, distal K_A type channel (K_A_4):
IAd =gAda4b(Vm-EK)
EK = -85 mV
ainf = 1/{exp[(-Vm-15)/8]+1}
taua = 0.15ms
binf = 1/{exp[(Vm+56)/8]+1}
taub = 5ms if Vm<-30 mV and 5+0.26(Vm+30) if Vm>30 mV
K_DR channel (K_DR_W):
IDR =gDRn4(Vm-EK)
EK = -85mV
alphan = (-0.018Vm)/[exp(Vm/-25)-1]
betan = 0.0036(Vm-10)/{exp[(Vm-10)/12]-1}
In the axon, Na+ channels were identical as for the somatodendritic membrane, while the DR-type K+ channel was obtained from Traub et al. (1994):
K_DRA channel (K_DRA_T):c. Ca dynamics:IDRA =gDRAnax4(Vm-EK)
EK = -85mV
alphan(ax)= -0.03(Vm+47.8)/{exp[(Vm+47.8)/-5]-1}
betan(ax) = 0.45exp[(Vm+53.0)/-40]
As described by Warman et al. (1994) and Borg-Graham (1998), the [Ca]i was simulated with two different Ca pools with different time constants, tau1 = 0.9 ms for the calculation of ECa and modulating the C-type K+ current and tau2 = 1 s for the AHP-type K+ current, as follows:
where taui is the i-th calcium pool removal time constant, fi is the fraction of Ca influx affecting the i-th pool (f1=0.7, f2=0.024), w is the thickness of the diffusion shell (1 micron), A is the compartment area, z is the valence of the calcium ion and F is Faraday's constant.
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